Source color gamuts and target color gamuts can generally be represented in 3D linear color spaces, such as a RGB or CIEXYZ color spaces.
The CIE XYZ color space was deliberately designed so that the Y parameter was a measure of the brightness or luminance of a color. It is known that each color M represented by three color coordinates X,Y,Z in such a color space has a chromaticity x,y that can be represented by a chromaticity point MC in a chromaticity plane, wherein this chromaticity x, y is calculated as follows:
      x    =          X              X        +        Y        +        Z                  y    =          Y              X        +        Y        +        Z            
As illustrated in FIG. 1, it is then common to represent the chromaticity of a color in this chromaticity plane xy. The derived 3D color space specified by x, y, and Y is known as the CIE xyY color space and is also widely used to specify colors in practice.
Note that in a La*b* perceptual non-linear color space, a*b* planes are not chromaticity planes but rather chrominance planes.
Reversely, note that the X and Z coordinates representing this color M in the CIE XYZ color space can be calculated back from the chromaticity values x and y and from Y as follows:
      X    =                  Y        y            ⁢      x            Z    =                  Y        y            ⁢              (                  1          -          x          -          y                )            
Note that any straight line in the chromaticity plane xy corresponds to a plane comprising the origin K of the CIE XYZ color space. As a matter of fact, replacing x and y by their values in any equation of a straight line in the chromaticity plane (i.e.: x+a.y+=0) will give the following equation of a plane in the XYZ color space (namely: (1+b).X+(a+b).Y+b.Z=0).
Similarly, any point in the chromaticity plane xy corresponds to a straight line comprising the origin K of the CIE XYZ color space. As a matter of fact, having fixed x=x0 and y=y0 in the chromaticity plane will give the following set of two linear equations X=f(Y); Z=f′(Y) defining a straight line in the XYZ color space, namely: X=(x0/y0).Y; Z=[(1−x0−y0)/y0].Y.
The above two correspondences can be for instance applied to a cube in the XYZ color space having the following eight vertices: Black Point K corresponding to the origin of the XYZ color space, a first primary color R, a second primary color G, a third primary color B, a first secondary color C combining the second and the third primary colors, a second secondary color M combining the third and the first primary colors, a third secondary color Y combining the first and the second primary colors, and a white color O combining the three primary colors. Planes of the CIE XYZ color space that are defined as including OGBC, OBRM and ORGY will then correspond to the three sides of a triangle in the xy chromaticity diagram, i.e. respectively GCBC, BCRC and RCGC. The diagonal OW of this cube will correspond to a point WC positioned roughly at the center of this triangle. Any point MC located inside this triangle will correspond to a straight line passing through K and the corresponding color M in the XYZ color space, and this straight line will intersect at an intersecting point I″ of the surface of the cube.
For mapping colors of an image, it is known to use such a chromaticity plane. See for instance the document US2015/221281. More specifically, it is known to map each color of such an image along a mapping straight line comprising the chromaticity point of this color and the chromaticity point of a white point, and still more specifically to map this color within a mapping segment of this mapping straight line. See for instance the document US2011/249016. The article entitled “A Gamut Expansion Algorithm Based on Saturation for Wide-gamut Displays”, by Gang Song et al., published in IEEE in 2010 discloses also such a method.